Can PCA work when the number of observations is smaller than the number of dimensions? [duplicate]

I understand how principal component analysis works. However, in a financial time series sense, I do not understand why the number of observations should be larger than the number of dimensions. I am having twenty securities (dimensions in this case) for ten time periods and I am told that PCA won't work here. Why wouldn't it work? Also, how does asymptotic principal component analysis help to solve this problem?

Can someone please explain this? If possible try to use less mathematical jargon (except for linear algebra basics such as eigenvalues/vectors). If it is not possible to explain it without using jargon, please go ahead and I will take my time and try to understand it.

• 1) Linear PCA does not require n>p because PCA is not afraid of singular data. This was answered on this site many times. 2) stats.stackexchange.com/a/43224/3277 is a question on Asymptotic PCA. This form of PCA seems to be a special way of use PCA in time series analysis. Jun 18 '14 at 7:23
• Closely related stats.stackexchange.com/questions/2772/…
– Momo
Jun 18 '14 at 11:47
• @ttnphns: Are you sure you gave the link you wanted to give? It seems unrelated to "asymptotic PCA", whatever it means. Jun 18 '14 at 22:08
• Yes, my link was erratum. The correct link, the one I really meant, is given by Momo. Thanks, @amoeba. Jun 19 '14 at 5:57
• Thanks for the thread. I have read that link and the answers there does not explain why should the number of observations be higher than the number of dimensions. I have searched this forum and I am not able to find solution to this. I'd be thankful if someone could explain this to me. Jun 19 '14 at 7:19